task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-mc-social-golfers-l6-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 6 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 49 golfers (numbered 0..48) for 8 weeks. Every week the golfers are split into 7 groups (numbered 0..6) of exactly 7 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_7]} where week_t is a list of 49 integers an... | {"n_groups": 7, "group_size": 7, "n_weeks": 8, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6, 6, 0, 1, 2, 3, 4, 5, 5, 6, 0, 1, 2, 3, 4, 4, 5, 6, 0, 1, 2, 3, 3, 4, 5, 6, 0, 1, 2, 2, 3, 4, 5, 6, 0, 1, 1, 2, 3, 4, 5, 6, 0], [0, 1, 2... | 1 |
construct-mc-social-golfers-l6-s3 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 6 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 49 golfers (numbered 0..48) for 6 weeks. Every week the golfers are split into 7 groups (numbered 0..6) of exactly 7 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 49 integers an... | {"n_groups": 7, "group_size": 7, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6, 6, 0, 1, 2, 3, 4, 5, 5, 6, 0, 1, 2, 3, 4, 4, 5, 6, 0, 1, 2, 3, 3, 4, 5, 6, 0, 1, 2, 2, 3, 4, 5, 6, 0, 1, 1, 2, 3, 4, 5, 6, 0], [0, 1, 2... | 1 |
construct-mc-van-der-waerden-l1-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 1 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 8 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 8 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_8]}: 8 integers in 0..1; the i-... | {"k": 2, "L": 3, "n": 8, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 1, 1, 0]} | 1 |
construct-mc-van-der-waerden-l1-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 1 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 7 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 7 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_7]}: 7 integers in 0..1; the i-... | {"k": 2, "L": 3, "n": 7, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 1, 1]} | 1 |
construct-mc-van-der-waerden-l1-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 1 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 6 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 6 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_6]}: 6 integers in 0..1; the i-... | {"k": 2, "L": 3, "n": 6, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 1]} | 1 |
construct-mc-van-der-waerden-l2-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 20 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 20 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_20]}: 20 integers in 0..2; th... | {"k": 3, "L": 3, "n": 20, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 0]} | 1 |
construct-mc-van-der-waerden-l2-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 20 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 20 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_20]}: 20 integers in 0..1; th... | {"k": 2, "L": 4, "n": 20, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]} | 1 |
construct-mc-van-der-waerden-l2-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 15 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 15 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_15]}: 15 integers in 0..2; th... | {"k": 3, "L": 3, "n": 15, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2]} | 1 |
construct-mc-van-der-waerden-l2-s3 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 18 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 18 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_18]}: 18 integers in 0..2; th... | {"k": 3, "L": 3, "n": 18, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0]} | 1 |
construct-mc-van-der-waerden-l2-s4 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 24 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 24 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_24]}: 24 integers in 0..1; th... | {"k": 2, "L": 4, "n": 24, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]} | 1 |
construct-mc-van-der-waerden-l2-s5 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 2 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 28 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 28 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_28]}: 28 integers in 0..1; th... | {"k": 2, "L": 4, "n": 28, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]} | 1 |
construct-mc-van-der-waerden-l3-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 32 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 32 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_32]}: 32 integers in 0..1; th... | {"k": 2, "L": 4, "n": 32, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]} | 1 |
construct-mc-van-der-waerden-l3-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 30 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 30 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_30]}: 30 integers in 0..1; th... | {"k": 2, "L": 4, "n": 30, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]} | 1 |
construct-mc-van-der-waerden-l3-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 26 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 26 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_26]}: 26 integers in 0..2; th... | {"k": 3, "L": 3, "n": 26, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0]} | 1 |
construct-mc-van-der-waerden-l3-s3 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 24 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 24 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_24]}: 24 integers in 0..2; th... | {"k": 3, "L": 3, "n": 24, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 0, 0, 1, 2, 2]} | 1 |
construct-mc-van-der-waerden-l3-s4 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 22 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 22 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_22]}: 22 integers in 0..2; th... | {"k": 3, "L": 3, "n": 22, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 0, 0, 1]} | 1 |
construct-mc-van-der-waerden-l3-s5 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 3 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 34 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 34 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_34]}: 34 integers in 0..1; th... | {"k": 2, "L": 4, "n": 34, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]} | 1 |
construct-mc-van-der-waerden-l4-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 60 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 60 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_60]}: 60 integers in 0..2; th... | {"k": 3, "L": 4, "n": 60, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 0]} | 1 |
construct-mc-van-der-waerden-l4-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 45 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 45 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_45]}: 45 integers in 0..3; th... | {"k": 4, "L": 3, "n": 45, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 2, 0, 2, 1, 1, 0, 2, 0, 3, 3, 0, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 3, 3, 2, 3, 3, 1, 1, 2, 2]} | 1 |
construct-mc-van-der-waerden-l4-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 100 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 100 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_100]}: 100 integers in 0..1... | {"k": 2, "L": 5, "n": 100, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]} | 1 |
construct-mc-van-der-waerden-l4-s3 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 60 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 60 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_60]}: 60 integers in 0..1; th... | {"k": 2, "L": 5, "n": 60, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]} | 1 |
construct-mc-van-der-waerden-l4-s4 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 50 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 50 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_50]}: 50 integers in 0..3; th... | {"k": 4, "L": 3, "n": 50, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 2, 0, 2, 1, 1, 0, 2, 0, 3, 3, 0, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 3, 3, 2, 3, 3, 1, 1, 2, 2, 3, 3, 2, 3, 3]} | 1 |
construct-mc-van-der-waerden-l4-s5 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 40 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 40 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_40]}: 40 integers in 0..3; th... | {"k": 4, "L": 3, "n": 40, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 2, 0, 2, 1, 1, 0, 2, 0, 3, 3, 0, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 3, 3, 2, 3]} | 1 |
construct-mc-van-der-waerden-l4-s6 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 80 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 80 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_80]}: 80 integers in 0..1; th... | {"k": 2, "L": 5, "n": 80, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]} | 1 |
construct-mc-van-der-waerden-l4-s7 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 4 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 80 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 80 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_80]}: 80 integers in 0..2; th... | {"k": 3, "L": 4, "n": 80, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1]} | 1 |
construct-mc-van-der-waerden-l5-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 120 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 120 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_120]}: 120 integers in 0..1... | {"k": 2, "L": 5, "n": 120, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1,... | 1 |
construct-mc-van-der-waerden-l5-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 135 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 135 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_135]}: 135 integers in 0..1... | {"k": 2, "L": 5, "n": 135, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1,... | 1 |
construct-mc-van-der-waerden-l5-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 60 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 60 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_60]}: 60 integers in 0..3; th... | {"k": 4, "L": 3, "n": 60, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2, 0, 2, 0, 0, 1, 0, 2, 3, 3, 0, 2, 3, 2, 3, 1, 2, 2, 3, 1, 0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2, 0, 2, 0, 0, 1]} | 1 |
construct-mc-van-der-waerden-l5-s3 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 65 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 65 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_65]}: 65 integers in 0..3; th... | {"k": 4, "L": 3, "n": 65, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2, 0, 2, 0, 0, 1, 0, 2, 3, 3, 0, 2, 3, 2, 3, 1, 2, 2, 3, 1, 0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2, 0, 2, 0, 0, 1, 0, 2, 3, 3, 0]} | 1 |
construct-mc-van-der-waerden-l5-s4 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 200 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 200 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_200]}: 200 integers in 0..2... | {"k": 3, "L": 4, "n": 200, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2,... | 1 |
construct-mc-van-der-waerden-l5-s5 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 100 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 100 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_100]}: 100 integers in 0..2... | {"k": 3, "L": 4, "n": 100, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2]} | 1 |
construct-mc-van-der-waerden-l5-s6 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 150 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 150 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_150]}: 150 integers in 0..1... | {"k": 2, "L": 5, "n": 150, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,... | 1 |
construct-mc-van-der-waerden-l5-s7 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 55 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 55 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_55]}: 55 integers in 0..3; th... | {"k": 4, "L": 3, "n": 55, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2, 0, 2, 0, 0, 1, 0, 2, 3, 3, 0, 2, 3, 2, 3, 1, 2, 2, 3, 1, 0, 1, 1, 3, 1, 3, 3, 0, 0, 2, 1, 0, 0, 3, 1, 1, 2, 2]} | 1 |
construct-mc-van-der-waerden-l5-s8 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 5 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 150 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 150 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_150]}: 150 integers in 0..2... | {"k": 3, "L": 4, "n": 150, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2,... | 1 |
construct-mc-van-der-waerden-l6-s0 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 165 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 165 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_165]}: 165 integers in 0..1... | {"k": 2, "L": 5, "n": 165, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1,... | 1 |
construct-mc-van-der-waerden-l6-s1 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 70 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 70 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_70]}: 70 integers in 0..3; th... | {"k": 4, "L": 3, "n": 70, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 3, 3, 0, 3, 0, 0, 2, 0, 3, 1, 1, 0, 3, 1, 3, 1, 2, 3, 3, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 3, 2, 0, 0, 1, 2, 2, 3, 3, 0, 3, 0, 0, 2, 0, 3, 1, 1, 0, 3, 1, 3, 1, 2, 3, 3, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0]} | 1 |
construct-mc-van-der-waerden-l6-s2 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 73 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 73 such that a, a+d, ..., a+2*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_73]}: 73 integers in 0..3; th... | {"k": 4, "L": 3, "n": 73, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 3, 3, 0, 3, 0, 0, 2, 0, 3, 1, 1, 0, 3, 1, 3, 1, 2, 3, 3, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 3, 2, 0, 0, 1, 2, 2, 3, 3, 0, 3, 0, 0, 2, 0, 3, 1, 1, 0, 3, 1, 3, 1, 2, 3, 3, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 3, 2]} | 1 |
construct-mc-van-der-waerden-l6-s3 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 500 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 6: no a >= 1, d >= 1 with a + 5*d <= 500 such that a, a+d, ..., a+5*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_500]}: 500 integers in 0..1... | {"k": 2, "L": 6, "n": 500, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1,... | 1 |
construct-mc-van-der-waerden-l6-s4 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 700 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 700 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_700]}: 700 integers in 0..2... | {"k": 3, "L": 5, "n": 700, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 2, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 2, 0, 2, 2, 0, 0, 0,... | 1 |
construct-mc-van-der-waerden-l6-s5 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 291 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 291 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_291]}: 291 integers in 0..2... | {"k": 3, "L": 4, "n": 291, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2,... | 1 |
construct-mc-van-der-waerden-l6-s6 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 600 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 6: no a >= 1, d >= 1 with a + 5*d <= 600 such that a, a+d, ..., a+5*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_600]}: 600 integers in 0..1... | {"k": 2, "L": 6, "n": 600, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1,... | 1 |
construct-mc-van-der-waerden-l6-s7 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 695 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 6: no a >= 1, d >= 1 with a + 5*d <= 695 such that a, a+d, ..., a+5*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_695]}: 695 integers in 0..1... | {"k": 2, "L": 6, "n": 695, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1,... | 1 |
construct-mc-van-der-waerden-l6-s8 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 250 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 250 such that a, a+d, ..., a+3*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_250]}: 250 integers in 0..2... | {"k": 3, "L": 4, "n": 250, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2,... | 1 |
construct-mc-van-der-waerden-l6-s9 | construct | mc_van_der_waerden | van_der_waerden_colouring | combinatorics | competition | 6 | MathConstraint/van_der_waerden | CC-BY-4.0 | [
"np_search"
] | Colour the integers 1, 2, ..., 177 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 5: no a >= 1, d >= 1 with a + 4*d <= 177 such that a, a+d, ..., a+4*d all have the same colour.
Find such a colouring.
Answer format: {"colors": [c_1, ..., c_177]}: 177 integers in 0..1... | {"k": 2, "L": 5, "n": 177, "family": "mc_van_der_waerden", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1,... | 1 |
construct-mc-vertex-cover-l1-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 33 edges:
(0,6), (0,14), (1,6), (1,12), (1,15), (1,19), (2,5), (2,11), (2,13), (2,19), (3,6), (3,17), (4,8), (4,19), (5,6), (5,19), (7,9), (8,10), (8,12), (8,15), (8,17), (8,19), (9,12), (9,14), (9,16), (9,18), (9,19), (11,18), (12,16), (13,18), (13,19), (14,16), (17,18)
Fin... | {"n": 20, "k": 11, "edges": [[0, 6], [0, 14], [1, 6], [1, 12], [1, 15], [1, 19], [2, 5], [2, 11], [2, 13], [2, 19], [3, 6], [3, 17], [4, 8], [4, 19], [5, 6], [5, 19], [7, 9], [8, 10], [8, 12], [8, 15], [8, 17], [8, 19], [9, 12], [9, 14], [9, 16], [9, 18], [9, 19], [11, 18], [12, 16], [13, 18], [13, 19], [14, 16], [17, ... | null | null | null | {"cover": [1, 2, 3, 6, 8, 9, 13, 14, 16, 18, 19]} | 1 |
construct-mc-vertex-cover-l1-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 31 edges:
(0,6), (1,4), (1,12), (2,7), (3,9), (3,12), (3,17), (3,18), (4,6), (4,10), (4,14), (5,6), (5,19), (6,7), (6,11), (6,15), (6,16), (7,11), (7,16), (7,17), (8,14), (8,16), (9,12), (9,13), (9,19), (10,12), (10,18), (12,17), (13,15), (13,16), (15,16)
Find a vertex cover... | {"n": 20, "k": 11, "edges": [[0, 6], [1, 4], [1, 12], [2, 7], [3, 9], [3, 12], [3, 17], [3, 18], [4, 6], [4, 10], [4, 14], [5, 6], [5, 19], [6, 7], [6, 11], [6, 15], [6, 16], [7, 11], [7, 16], [7, 17], [8, 14], [8, 16], [9, 12], [9, 13], [9, 19], [10, 12], [10, 18], [12, 17], [13, 15], [13, 16], [15, 16]], "family": "m... | null | null | null | {"cover": [3, 4, 6, 7, 10, 12, 13, 14, 15, 16, 19]} | 1 |
construct-mc-vertex-cover-l1-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 32 edges:
(0,8), (0,14), (1,9), (1,12), (1,19), (2,4), (2,9), (3,10), (3,15), (4,5), (4,8), (4,10), (4,15), (5,15), (6,8), (6,18), (7,9), (7,10), (7,16), (8,10), (8,11), (8,14), (8,15), (8,16), (8,18), (9,16), (9,17), (9,19), (10,11), (11,13), (12,17), (14,16)
Find a vertex ... | {"n": 20, "k": 11, "edges": [[0, 8], [0, 14], [1, 9], [1, 12], [1, 19], [2, 4], [2, 9], [3, 10], [3, 15], [4, 5], [4, 8], [4, 10], [4, 15], [5, 15], [6, 8], [6, 18], [7, 9], [7, 10], [7, 16], [8, 10], [8, 11], [8, 14], [8, 15], [8, 16], [8, 18], [9, 16], [9, 17], [9, 19], [10, 11], [11, 13], [12, 17], [14, 16]], "famil... | null | null | null | {"cover": [1, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15]} | 1 |
construct-mc-vertex-cover-l1-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 29 edges:
(0,8), (0,19), (1,6), (1,9), (1,17), (1,18), (2,3), (3,7), (3,13), (3,18), (5,12), (5,14), (5,17), (6,11), (6,14), (8,10), (8,12), (8,15), (9,15), (9,18), (12,18), (12,19), (13,15), (14,15), (15,16), (15,17), (15,19), (16,18), (17,18)
Find a vertex cover of G with ... | {"n": 20, "k": 11, "edges": [[0, 8], [0, 19], [1, 6], [1, 9], [1, 17], [1, 18], [2, 3], [3, 7], [3, 13], [3, 18], [5, 12], [5, 14], [5, 17], [6, 11], [6, 14], [8, 10], [8, 12], [8, 15], [9, 15], [9, 18], [12, 18], [12, 19], [13, 15], [14, 15], [15, 16], [15, 17], [15, 19], [16, 18], [17, 18]], "family": "mc_vertex_cove... | null | null | null | {"cover": [1, 3, 5, 6, 8, 10, 11, 15, 17, 18, 19]} | 1 |
construct-mc-vertex-cover-l1-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 24 edges:
(0,10), (0,17), (0,18), (1,8), (1,19), (2,9), (2,16), (3,10), (3,14), (3,16), (3,17), (4,9), (4,14), (4,17), (5,18), (6,9), (7,18), (8,9), (8,12), (8,14), (10,12), (10,14), (10,18), (12,14)
Find a vertex cover of G with at most 11 vertices: a set of vertices that c... | {"n": 20, "k": 11, "edges": [[0, 10], [0, 17], [0, 18], [1, 8], [1, 19], [2, 9], [2, 16], [3, 10], [3, 14], [3, 16], [3, 17], [4, 9], [4, 14], [4, 17], [5, 18], [6, 9], [7, 18], [8, 9], [8, 12], [8, 14], [10, 12], [10, 14], [10, 18], [12, 14]], "family": "mc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [0, 5, 8, 9, 10, 11, 14, 16, 17, 18, 19]} | 1 |
construct-mc-vertex-cover-l1-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 35 edges:
(0,5), (0,6), (0,13), (1,2), (1,12), (2,13), (2,15), (3,8), (3,12), (3,19), (4,6), (4,14), (4,15), (4,17), (4,18), (5,7), (5,8), (5,9), (5,11), (6,12), (6,13), (6,14), (6,15), (7,15), (7,16), (8,17), (9,14), (9,15), (10,13), (12,13), (13,15), (13,19), (15,16), (15,1... | {"n": 20, "k": 11, "edges": [[0, 5], [0, 6], [0, 13], [1, 2], [1, 12], [2, 13], [2, 15], [3, 8], [3, 12], [3, 19], [4, 6], [4, 14], [4, 15], [4, 17], [4, 18], [5, 7], [5, 8], [5, 9], [5, 11], [6, 12], [6, 13], [6, 14], [6, 15], [7, 15], [7, 16], [8, 17], [9, 14], [9, 15], [10, 13], [12, 13], [13, 15], [13, 19], [15, 16... | null | null | null | {"cover": [2, 3, 5, 6, 12, 13, 14, 15, 16, 17, 18]} | 1 |
construct-mc-vertex-cover-l1-s6 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 32 edges:
(0,2), (0,7), (0,13), (0,15), (1,5), (1,7), (1,10), (1,17), (3,6), (3,12), (3,16), (3,19), (4,6), (4,18), (4,19), (5,6), (5,12), (5,17), (7,11), (7,19), (8,10), (8,11), (10,12), (10,16), (11,16), (11,17), (12,13), (12,16), (13,16), (14,18), (15,19), (16,17)
Find a ... | {"n": 20, "k": 11, "edges": [[0, 2], [0, 7], [0, 13], [0, 15], [1, 5], [1, 7], [1, 10], [1, 17], [3, 6], [3, 12], [3, 16], [3, 19], [4, 6], [4, 18], [4, 19], [5, 6], [5, 12], [5, 17], [7, 11], [7, 19], [8, 10], [8, 11], [10, 12], [10, 16], [11, 16], [11, 17], [12, 13], [12, 16], [13, 16], [14, 18], [15, 19], [16, 17]],... | null | null | null | {"cover": [0, 1, 4, 6, 7, 8, 12, 16, 17, 18, 19]} | 1 |
construct-mc-vertex-cover-l1-s7 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 31 edges:
(0,2), (0,5), (0,6), (0,10), (1,3), (1,5), (1,17), (1,18), (2,9), (2,15), (3,6), (3,11), (3,12), (4,11), (4,12), (5,15), (5,18), (6,8), (6,16), (6,17), (7,13), (7,14), (7,17), (8,12), (9,16), (10,12), (10,18), (12,13), (12,17), (12,18), (16,18)
Find a vertex cover ... | {"n": 20, "k": 11, "edges": [[0, 2], [0, 5], [0, 6], [0, 10], [1, 3], [1, 5], [1, 17], [1, 18], [2, 9], [2, 15], [3, 6], [3, 11], [3, 12], [4, 11], [4, 12], [5, 15], [5, 18], [6, 8], [6, 16], [6, 17], [7, 13], [7, 14], [7, 17], [8, 12], [9, 16], [10, 12], [10, 18], [12, 13], [12, 17], [12, 18], [16, 18]], "family": "mc... | null | null | null | {"cover": [0, 1, 2, 6, 7, 10, 11, 12, 15, 16, 18]} | 1 |
construct-mc-vertex-cover-l1-s8 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,4), (0,7), (0,9), (0,10), (1,17), (2,8), (2,11), (3,15), (4,6), (4,7), (4,12), (4,19), (5,13), (6,12), (6,18), (7,11), (7,16), (8,16), (9,12), (9,13), (9,15), (10,13), (10,18), (11,12), (11,13), (12,17), (13,14), (13,19), (16,17), (17,19)
Find a vertex cover of ... | {"n": 20, "k": 11, "edges": [[0, 4], [0, 7], [0, 9], [0, 10], [1, 17], [2, 8], [2, 11], [3, 15], [4, 6], [4, 7], [4, 12], [4, 19], [5, 13], [6, 12], [6, 18], [7, 11], [7, 16], [8, 16], [9, 12], [9, 13], [9, 15], [10, 13], [10, 18], [11, 12], [11, 13], [12, 17], [13, 14], [13, 19], [16, 17], [17, 19]], "family": "mc_ver... | null | null | null | {"cover": [0, 1, 2, 4, 7, 12, 13, 15, 16, 18, 19]} | 1 |
construct-mc-vertex-cover-l1-s9 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,7), (1,4), (1,8), (2,12), (2,18), (3,8), (3,13), (4,6), (4,7), (4,11), (4,19), (5,8), (5,12), (5,14), (5,15), (5,16), (5,19), (6,16), (7,9), (7,11), (7,18), (8,16), (8,19), (9,13), (10,14), (11,12), (12,17), (12,19), (14,16), (14,19)
Find a vertex cover of G wit... | {"n": 20, "k": 11, "edges": [[0, 7], [1, 4], [1, 8], [2, 12], [2, 18], [3, 8], [3, 13], [4, 6], [4, 7], [4, 11], [4, 19], [5, 8], [5, 12], [5, 14], [5, 15], [5, 16], [5, 19], [6, 16], [7, 9], [7, 11], [7, 18], [8, 16], [8, 19], [9, 13], [10, 14], [11, 12], [12, 17], [12, 19], [14, 16], [14, 19]], "family": "mc_vertex_c... | null | null | null | {"cover": [2, 4, 5, 7, 8, 12, 13, 14, 16, 18, 19]} | 1 |
construct-mc-vertex-cover-l2-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 73 edges:
(0,1), (0,2), (0,6), (0,10), (0,11), (0,13), (0,14), (0,16), (0,24), (0,25), (0,27), (1,8), (1,15), (1,23), (1,25), (1,26), (2,4), (2,12), (2,22), (3,4), (3,6), (3,7), (3,11), (3,13), (3,26), (4,15), (4,21), (4,24), (5,10), (5,25), (5,27), (5,28), (6,24), (6,25), (6... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 2], [0, 6], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 24], [0, 25], [0, 27], [1, 8], [1, 15], [1, 23], [1, 25], [1, 26], [2, 4], [2, 12], [2, 22], [3, 4], [3, 6], [3, 7], [3, 11], [3, 13], [3, 26], [4, 15], [4, 21], [4, 24], [5, 10], [5, 25], [5, 27], [5, 28], [6, 24], [6... | null | null | null | {"cover": [0, 1, 3, 4, 8, 10, 12, 13, 14, 15, 18, 19, 21, 22, 24, 25, 27, 28]} | 1 |
construct-mc-vertex-cover-l2-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 82 edges:
(0,3), (0,5), (0,11), (0,13), (0,19), (0,20), (1,4), (1,7), (1,9), (1,10), (1,12), (1,13), (1,22), (2,5), (2,7), (2,10), (2,11), (2,12), (2,13), (2,14), (2,15), (2,17), (2,19), (2,22), (2,24), (2,27), (2,29), (3,7), (3,13), (3,14), (3,22), (3,25), (3,27), (4,6), (4,... | {"n": 30, "k": 18, "edges": [[0, 3], [0, 5], [0, 11], [0, 13], [0, 19], [0, 20], [1, 4], [1, 7], [1, 9], [1, 10], [1, 12], [1, 13], [1, 22], [2, 5], [2, 7], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 19], [2, 22], [2, 24], [2, 27], [2, 29], [3, 7], [3, 13], [3, 14], [3, 22], [3, 25], [3, 27], [4... | null | null | null | {"cover": [0, 1, 2, 5, 6, 7, 8, 9, 13, 14, 18, 19, 22, 23, 24, 25, 27, 28]} | 1 |
construct-mc-vertex-cover-l2-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 61 edges:
(0,19), (0,28), (1,14), (1,18), (1,25), (1,27), (2,13), (2,15), (2,16), (2,21), (2,26), (2,27), (3,4), (3,9), (3,18), (3,20), (3,24), (4,8), (4,9), (4,13), (4,19), (4,25), (5,8), (6,7), (6,10), (6,17), (7,11), (7,25), (8,13), (8,18), (8,27), (8,29), (9,13), (10,14),... | {"n": 30, "k": 18, "edges": [[0, 19], [0, 28], [1, 14], [1, 18], [1, 25], [1, 27], [2, 13], [2, 15], [2, 16], [2, 21], [2, 26], [2, 27], [3, 4], [3, 9], [3, 18], [3, 20], [3, 24], [4, 8], [4, 9], [4, 13], [4, 19], [4, 25], [5, 8], [6, 7], [6, 10], [6, 17], [7, 11], [7, 25], [8, 13], [8, 18], [8, 27], [8, 29], [9, 13], ... | null | null | null | {"cover": [0, 2, 3, 4, 6, 7, 8, 10, 13, 14, 16, 18, 19, 20, 21, 23, 25, 27]} | 1 |
construct-mc-vertex-cover-l2-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 68 edges:
(0,1), (0,6), (0,7), (0,9), (0,13), (0,16), (0,22), (0,23), (0,25), (0,26), (1,3), (1,8), (1,9), (2,6), (2,11), (2,15), (2,16), (2,17), (2,19), (2,23), (3,10), (3,22), (3,26), (3,29), (4,6), (4,19), (4,22), (5,7), (5,14), (7,11), (7,21), (7,24), (7,26), (7,27), (8,1... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 6], [0, 7], [0, 9], [0, 13], [0, 16], [0, 22], [0, 23], [0, 25], [0, 26], [1, 3], [1, 8], [1, 9], [2, 6], [2, 11], [2, 15], [2, 16], [2, 17], [2, 19], [2, 23], [3, 10], [3, 22], [3, 26], [3, 29], [4, 6], [4, 19], [4, 22], [5, 7], [5, 14], [7, 11], [7, 21], [7, 24], [7, 26], [7, ... | null | null | null | {"cover": [0, 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 21, 22, 23, 24, 25, 28]} | 1 |
construct-mc-vertex-cover-l2-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 82 edges:
(0,2), (0,8), (0,17), (0,22), (1,3), (1,5), (1,16), (1,22), (2,5), (2,9), (2,12), (2,15), (2,25), (2,26), (2,28), (3,8), (3,26), (4,13), (4,27), (4,29), (5,6), (5,12), (5,16), (5,19), (5,20), (5,21), (5,25), (5,28), (6,17), (6,18), (6,23), (6,24), (6,27), (6,29), (7... | {"n": 30, "k": 18, "edges": [[0, 2], [0, 8], [0, 17], [0, 22], [1, 3], [1, 5], [1, 16], [1, 22], [2, 5], [2, 9], [2, 12], [2, 15], [2, 25], [2, 26], [2, 28], [3, 8], [3, 26], [4, 13], [4, 27], [4, 29], [5, 6], [5, 12], [5, 16], [5, 19], [5, 20], [5, 21], [5, 25], [5, 28], [6, 17], [6, 18], [6, 23], [6, 24], [6, 27], [6... | null | null | null | {"cover": [2, 3, 5, 7, 8, 12, 13, 14, 16, 17, 18, 22, 23, 24, 26, 27, 28, 29]} | 1 |
construct-mc-vertex-cover-l2-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 76 edges:
(0,1), (0,4), (0,8), (0,18), (0,20), (0,25), (0,28), (1,10), (1,12), (1,15), (1,19), (1,21), (1,28), (2,4), (2,14), (2,22), (2,26), (2,27), (3,6), (4,10), (4,17), (4,25), (5,6), (5,7), (5,9), (5,17), (5,19), (5,23), (5,28), (6,8), (6,14), (6,15), (6,16), (6,18), (6,... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 4], [0, 8], [0, 18], [0, 20], [0, 25], [0, 28], [1, 10], [1, 12], [1, 15], [1, 19], [1, 21], [1, 28], [2, 4], [2, 14], [2, 22], [2, 26], [2, 27], [3, 6], [4, 10], [4, 17], [4, 25], [5, 6], [5, 7], [5, 9], [5, 17], [5, 19], [5, 23], [5, 28], [6, 8], [6, 14], [6, 15], [6, 16], [6,... | null | null | null | {"cover": [1, 2, 4, 5, 6, 8, 13, 15, 16, 18, 20, 21, 23, 24, 25, 26, 28, 29]} | 1 |
construct-mc-vertex-cover-l2-s6 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 79 edges:
(0,1), (0,2), (0,4), (0,5), (0,8), (0,22), (1,4), (1,7), (1,9), (1,10), (1,13), (1,15), (1,16), (1,21), (1,25), (2,8), (2,9), (2,11), (2,13), (2,16), (3,6), (3,8), (3,16), (3,19), (3,23), (3,24), (3,27), (4,5), (4,10), (4,18), (5,6), (5,7), (5,10), (5,20), (5,26), (... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 8], [0, 22], [1, 4], [1, 7], [1, 9], [1, 10], [1, 13], [1, 15], [1, 16], [1, 21], [1, 25], [2, 8], [2, 9], [2, 11], [2, 13], [2, 16], [3, 6], [3, 8], [3, 16], [3, 19], [3, 23], [3, 24], [3, 27], [4, 5], [4, 10], [4, 18], [5, 6], [5, 7], [5, 10], [5, 20], ... | null | null | null | {"cover": [0, 1, 2, 3, 5, 6, 7, 8, 10, 14, 16, 18, 20, 21, 22, 25, 28, 29]} | 1 |
construct-mc-vertex-cover-l2-s7 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 72 edges:
(0,1), (0,2), (0,9), (0,16), (0,17), (0,21), (1,8), (1,11), (1,19), (2,6), (2,28), (3,18), (3,22), (3,24), (3,28), (4,5), (4,10), (4,11), (4,23), (5,6), (5,11), (5,22), (5,25), (6,8), (6,15), (6,16), (6,20), (6,21), (6,26), (7,27), (8,10), (8,15), (8,17), (8,19), (8... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 2], [0, 9], [0, 16], [0, 17], [0, 21], [1, 8], [1, 11], [1, 19], [2, 6], [2, 28], [3, 18], [3, 22], [3, 24], [3, 28], [4, 5], [4, 10], [4, 11], [4, 23], [5, 6], [5, 11], [5, 22], [5, 25], [6, 8], [6, 15], [6, 16], [6, 20], [6, 21], [6, 26], [7, 27], [8, 10], [8, 15], [8, 17], [8... | null | null | null | {"cover": [0, 1, 4, 6, 8, 10, 11, 15, 16, 17, 18, 20, 22, 23, 24, 25, 27, 28]} | 1 |
construct-mc-vertex-cover-l2-s8 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 79 edges:
(0,1), (0,3), (0,5), (0,11), (0,14), (0,21), (0,22), (0,23), (0,24), (0,25), (1,15), (1,17), (1,28), (2,5), (2,14), (2,28), (3,4), (3,5), (3,14), (3,15), (3,21), (3,25), (4,9), (4,12), (5,8), (5,17), (5,22), (5,25), (5,28), (6,8), (6,17), (6,25), (7,8), (7,9), (7,10... | {"n": 30, "k": 18, "edges": [[0, 1], [0, 3], [0, 5], [0, 11], [0, 14], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [1, 15], [1, 17], [1, 28], [2, 5], [2, 14], [2, 28], [3, 4], [3, 5], [3, 14], [3, 15], [3, 21], [3, 25], [4, 9], [4, 12], [5, 8], [5, 17], [5, 22], [5, 25], [5, 28], [6, 8], [6, 17], [6, 25], [7, 8], [7, ... | null | null | null | {"cover": [0, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 20, 21, 25, 27, 28]} | 1 |
construct-mc-vertex-cover-l2-s9 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 74 edges:
(0,9), (0,13), (0,19), (0,26), (0,27), (1,2), (1,6), (1,7), (1,12), (1,15), (1,16), (1,19), (1,26), (1,28), (2,12), (2,14), (2,23), (2,28), (2,29), (3,6), (3,8), (3,11), (3,16), (3,21), (3,23), (4,11), (4,14), (4,19), (4,21), (5,9), (5,10), (5,12), (5,13), (5,24), (... | {"n": 30, "k": 18, "edges": [[0, 9], [0, 13], [0, 19], [0, 26], [0, 27], [1, 2], [1, 6], [1, 7], [1, 12], [1, 15], [1, 16], [1, 19], [1, 26], [1, 28], [2, 12], [2, 14], [2, 23], [2, 28], [2, 29], [3, 6], [3, 8], [3, 11], [3, 16], [3, 21], [3, 23], [4, 11], [4, 14], [4, 19], [4, 21], [5, 9], [5, 10], [5, 12], [5, 13], [... | null | null | null | {"cover": [0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 14, 19, 21, 22, 23, 24, 28, 29]} | 1 |
construct-mc-vertex-cover-l3-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 188 edges:
(0,11), (0,14), (0,18), (0,23), (0,24), (0,36), (0,39), (0,42), (1,4), (1,5), (1,16), (1,19), (1,20), (1,24), (1,42), (2,3), (2,4), (2,8), (2,12), (2,14), (2,24), (2,34), (2,37), (2,39), (2,40), (2,42), (3,4), (3,6), (3,10), (3,12), (3,18), (3,23), (3,31), (3,36), ... | {"n": 45, "k": 30, "edges": [[0, 11], [0, 14], [0, 18], [0, 23], [0, 24], [0, 36], [0, 39], [0, 42], [1, 4], [1, 5], [1, 16], [1, 19], [1, 20], [1, 24], [1, 42], [2, 3], [2, 4], [2, 8], [2, 12], [2, 14], [2, 24], [2, 34], [2, 37], [2, 39], [2, 40], [2, 42], [3, 4], [3, 6], [3, 10], [3, 12], [3, 18], [3, 23], [3, 31], [... | null | null | null | {"cover": [0, 1, 2, 3, 5, 6, 7, 9, 10, 12, 15, 16, 18, 19, 20, 22, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 43, 44]} | 1 |
construct-mc-vertex-cover-l3-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 187 edges:
(0,1), (0,4), (0,6), (0,8), (0,14), (0,15), (0,17), (0,25), (0,27), (0,30), (1,6), (1,9), (1,19), (1,22), (1,35), (1,43), (2,13), (2,24), (2,26), (2,28), (2,31), (2,32), (2,38), (2,43), (2,44), (3,16), (3,28), (3,30), (3,35), (3,38), (3,40), (4,10), (4,19), (4,41),... | {"n": 45, "k": 30, "edges": [[0, 1], [0, 4], [0, 6], [0, 8], [0, 14], [0, 15], [0, 17], [0, 25], [0, 27], [0, 30], [1, 6], [1, 9], [1, 19], [1, 22], [1, 35], [1, 43], [2, 13], [2, 24], [2, 26], [2, 28], [2, 31], [2, 32], [2, 38], [2, 43], [2, 44], [3, 16], [3, 28], [3, 30], [3, 35], [3, 38], [3, 40], [4, 10], [4, 19], ... | null | null | null | {"cover": [0, 1, 2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 36, 38, 41, 42, 43]} | 1 |
construct-mc-vertex-cover-l3-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 164 edges:
(0,13), (0,18), (0,29), (0,31), (0,32), (0,38), (1,4), (1,5), (1,6), (1,9), (1,11), (1,12), (1,16), (1,24), (1,26), (1,27), (1,42), (2,3), (2,4), (2,16), (2,24), (2,26), (2,33), (2,41), (3,15), (3,16), (3,18), (3,25), (3,31), (3,33), (3,35), (3,38), (3,42), (4,25),... | {"n": 45, "k": 30, "edges": [[0, 13], [0, 18], [0, 29], [0, 31], [0, 32], [0, 38], [1, 4], [1, 5], [1, 6], [1, 9], [1, 11], [1, 12], [1, 16], [1, 24], [1, 26], [1, 27], [1, 42], [2, 3], [2, 4], [2, 16], [2, 24], [2, 26], [2, 33], [2, 41], [3, 15], [3, 16], [3, 18], [3, 25], [3, 31], [3, 33], [3, 35], [3, 38], [3, 42], ... | null | null | null | {"cover": [0, 1, 2, 3, 6, 9, 12, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42]} | 1 |
construct-mc-vertex-cover-l3-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 174 edges:
(0,1), (0,3), (0,7), (0,9), (0,14), (0,15), (0,25), (0,26), (0,27), (0,31), (0,32), (0,41), (1,5), (1,12), (1,24), (1,26), (1,28), (1,33), (1,37), (2,11), (2,16), (2,38), (2,43), (3,24), (3,39), (3,40), (4,7), (4,16), (4,19), (4,21), (4,23), (4,26), (4,27), (4,36),... | {"n": 45, "k": 30, "edges": [[0, 1], [0, 3], [0, 7], [0, 9], [0, 14], [0, 15], [0, 25], [0, 26], [0, 27], [0, 31], [0, 32], [0, 41], [1, 5], [1, 12], [1, 24], [1, 26], [1, 28], [1, 33], [1, 37], [2, 11], [2, 16], [2, 38], [2, 43], [3, 24], [3, 39], [3, 40], [4, 7], [4, 16], [4, 19], [4, 21], [4, 23], [4, 26], [4, 27], ... | null | null | null | {"cover": [0, 1, 2, 4, 6, 9, 10, 12, 14, 15, 17, 18, 20, 22, 24, 25, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42]} | 1 |
construct-mc-vertex-cover-l3-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 178 edges:
(0,1), (0,8), (0,16), (0,23), (0,27), (0,31), (0,34), (1,2), (1,4), (1,5), (1,12), (1,27), (1,33), (1,34), (1,35), (1,36), (1,40), (2,7), (2,13), (2,19), (2,24), (2,33), (2,37), (3,5), (3,14), (3,21), (3,32), (3,34), (3,38), (3,44), (4,11), (4,20), (4,30), (4,36), ... | {"n": 45, "k": 30, "edges": [[0, 1], [0, 8], [0, 16], [0, 23], [0, 27], [0, 31], [0, 34], [1, 2], [1, 4], [1, 5], [1, 12], [1, 27], [1, 33], [1, 34], [1, 35], [1, 36], [1, 40], [2, 7], [2, 13], [2, 19], [2, 24], [2, 33], [2, 37], [3, 5], [3, 14], [3, 21], [3, 32], [3, 34], [3, 38], [3, 44], [4, 11], [4, 20], [4, 30], [... | null | null | null | {"cover": [1, 2, 3, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 20, 22, 23, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 43]} | 1 |
construct-mc-vertex-cover-l3-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 188 edges:
(0,12), (0,17), (0,19), (0,43), (1,5), (1,10), (1,12), (1,19), (1,20), (1,21), (1,24), (1,28), (1,30), (1,39), (1,40), (1,43), (2,10), (2,12), (2,14), (2,17), (2,18), (2,25), (2,30), (2,36), (2,37), (2,40), (3,18), (3,22), (3,32), (3,35), (3,39), (3,43), (4,14), (4... | {"n": 45, "k": 30, "edges": [[0, 12], [0, 17], [0, 19], [0, 43], [1, 5], [1, 10], [1, 12], [1, 19], [1, 20], [1, 21], [1, 24], [1, 28], [1, 30], [1, 39], [1, 40], [1, 43], [2, 10], [2, 12], [2, 14], [2, 17], [2, 18], [2, 25], [2, 30], [2, 36], [2, 37], [2, 40], [3, 18], [3, 22], [3, 32], [3, 35], [3, 39], [3, 43], [4, ... | null | null | null | {"cover": [1, 2, 3, 6, 7, 9, 11, 12, 14, 15, 16, 17, 18, 19, 24, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44]} | 1 |
construct-mc-vertex-cover-l3-s6 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 208 edges:
(0,2), (0,3), (0,4), (0,6), (0,17), (0,21), (0,30), (1,3), (1,4), (1,5), (1,15), (1,22), (1,42), (1,43), (2,5), (2,7), (2,10), (2,11), (2,18), (2,23), (2,26), (2,32), (2,33), (2,35), (2,39), (2,44), (3,25), (3,30), (3,31), (3,33), (3,35), (3,36), (3,38), (3,40), (4... | {"n": 45, "k": 30, "edges": [[0, 2], [0, 3], [0, 4], [0, 6], [0, 17], [0, 21], [0, 30], [1, 3], [1, 4], [1, 5], [1, 15], [1, 22], [1, 42], [1, 43], [2, 5], [2, 7], [2, 10], [2, 11], [2, 18], [2, 23], [2, 26], [2, 32], [2, 33], [2, 35], [2, 39], [2, 44], [3, 25], [3, 30], [3, 31], [3, 33], [3, 35], [3, 36], [3, 38], [3,... | null | null | null | {"cover": [2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 18, 21, 22, 23, 24, 25, 27, 29, 30, 32, 33, 34, 37, 39, 42, 43, 44]} | 1 |
construct-mc-vertex-cover-l3-s7 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 178 edges:
(0,3), (0,4), (0,9), (0,14), (0,15), (0,19), (0,20), (0,23), (0,24), (0,28), (0,31), (0,32), (1,6), (1,13), (1,20), (1,26), (1,37), (1,40), (2,3), (2,5), (2,18), (2,21), (2,33), (2,38), (2,43), (3,5), (3,8), (3,13), (3,23), (3,26), (3,28), (3,33), (3,38), (3,43), (... | {"n": 45, "k": 30, "edges": [[0, 3], [0, 4], [0, 9], [0, 14], [0, 15], [0, 19], [0, 20], [0, 23], [0, 24], [0, 28], [0, 31], [0, 32], [1, 6], [1, 13], [1, 20], [1, 26], [1, 37], [1, 40], [2, 3], [2, 5], [2, 18], [2, 21], [2, 33], [2, 38], [2, 43], [3, 5], [3, 8], [3, 13], [3, 23], [3, 26], [3, 28], [3, 33], [3, 38], [3... | null | null | null | {"cover": [0, 2, 3, 4, 6, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 31, 32, 36, 37, 38, 39, 40, 41, 43]} | 1 |
construct-mc-vertex-cover-l3-s8 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 154 edges:
(0,4), (0,5), (0,20), (1,5), (1,10), (1,13), (1,18), (1,21), (1,22), (1,35), (2,12), (2,28), (2,34), (2,38), (3,4), (3,7), (3,19), (3,21), (3,24), (3,25), (3,28), (3,30), (3,31), (3,34), (3,38), (4,13), (4,14), (4,19), (4,21), (4,22), (4,25), (4,33), (5,12), (5,19)... | {"n": 45, "k": 30, "edges": [[0, 4], [0, 5], [0, 20], [1, 5], [1, 10], [1, 13], [1, 18], [1, 21], [1, 22], [1, 35], [2, 12], [2, 28], [2, 34], [2, 38], [3, 4], [3, 7], [3, 19], [3, 21], [3, 24], [3, 25], [3, 28], [3, 30], [3, 31], [3, 34], [3, 38], [4, 13], [4, 14], [4, 19], [4, 21], [4, 22], [4, 25], [4, 33], [5, 12],... | null | null | null | {"cover": [4, 5, 6, 7, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 34, 35, 36, 37, 38, 41, 44]} | 1 |
construct-mc-vertex-cover-l3-s9 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 186 edges:
(0,2), (0,11), (0,19), (0,30), (0,32), (0,35), (0,38), (1,6), (1,14), (1,15), (1,26), (1,27), (1,33), (1,44), (2,4), (2,5), (2,6), (2,13), (2,23), (2,25), (2,26), (2,31), (2,36), (2,37), (2,38), (3,6), (3,7), (3,8), (3,12), (3,15), (3,23), (4,17), (4,22), (4,29), (... | {"n": 45, "k": 30, "edges": [[0, 2], [0, 11], [0, 19], [0, 30], [0, 32], [0, 35], [0, 38], [1, 6], [1, 14], [1, 15], [1, 26], [1, 27], [1, 33], [1, 44], [2, 4], [2, 5], [2, 6], [2, 13], [2, 23], [2, 25], [2, 26], [2, 31], [2, 36], [2, 37], [2, 38], [3, 6], [3, 7], [3, 8], [3, 12], [3, 15], [3, 23], [4, 17], [4, 22], [4... | null | null | null | {"cover": [1, 2, 4, 5, 6, 7, 8, 11, 12, 14, 15, 17, 19, 20, 22, 23, 24, 25, 28, 29, 30, 32, 35, 36, 37, 38, 39, 40, 41, 42]} | 1 |
construct-mc-vertex-cover-l4-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 327 edges:
(0,2), (0,5), (0,8), (0,16), (0,17), (0,21), (0,46), (0,50), (0,51), (1,2), (1,4), (1,12), (1,15), (1,36), (1,38), (1,40), (1,50), (1,55), (1,57), (2,9), (2,12), (2,28), (2,35), (2,38), (2,44), (2,45), (2,46), (2,52), (2,54), (2,55), (2,58), (3,12), (3,15), (3,20),... | {"n": 60, "k": 41, "edges": [[0, 2], [0, 5], [0, 8], [0, 16], [0, 17], [0, 21], [0, 46], [0, 50], [0, 51], [1, 2], [1, 4], [1, 12], [1, 15], [1, 36], [1, 38], [1, 40], [1, 50], [1, 55], [1, 57], [2, 9], [2, 12], [2, 28], [2, 35], [2, 38], [2, 44], [2, 45], [2, 46], [2, 52], [2, 54], [2, 55], [2, 58], [3, 12], [3, 15], ... | null | null | null | {"cover": [1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 23, 25, 26, 27, 29, 30, 33, 35, 36, 37, 39, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 58]} | 1 |
construct-mc-vertex-cover-l4-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 317 edges:
(0,4), (0,9), (0,31), (0,32), (0,35), (0,41), (0,45), (0,50), (0,54), (1,19), (1,20), (1,26), (1,29), (1,37), (1,40), (1,46), (1,52), (1,53), (2,3), (2,10), (2,17), (2,20), (2,21), (2,29), (2,32), (2,33), (2,34), (2,36), (2,46), (2,47), (3,4), (3,18), (3,19), (3,25... | {"n": 60, "k": 41, "edges": [[0, 4], [0, 9], [0, 31], [0, 32], [0, 35], [0, 41], [0, 45], [0, 50], [0, 54], [1, 19], [1, 20], [1, 26], [1, 29], [1, 37], [1, 40], [1, 46], [1, 52], [1, 53], [2, 3], [2, 10], [2, 17], [2, 20], [2, 21], [2, 29], [2, 32], [2, 33], [2, 34], [2, 36], [2, 46], [2, 47], [3, 4], [3, 18], [3, 19]... | null | null | null | {"cover": [0, 3, 4, 5, 6, 7, 9, 10, 12, 13, 16, 17, 18, 19, 20, 21, 22, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57]} | 1 |
construct-mc-vertex-cover-l4-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 321 edges:
(0,1), (0,3), (0,19), (0,25), (0,28), (0,41), (0,44), (0,56), (1,4), (1,17), (1,20), (1,26), (1,27), (1,31), (1,38), (1,49), (1,50), (1,51), (1,54), (1,58), (2,11), (2,12), (2,14), (2,16), (2,38), (2,39), (2,40), (2,48), (2,53), (2,55), (2,57), (3,7), (3,17), (3,24... | {"n": 60, "k": 41, "edges": [[0, 1], [0, 3], [0, 19], [0, 25], [0, 28], [0, 41], [0, 44], [0, 56], [1, 4], [1, 17], [1, 20], [1, 26], [1, 27], [1, 31], [1, 38], [1, 49], [1, 50], [1, 51], [1, 54], [1, 58], [2, 11], [2, 12], [2, 14], [2, 16], [2, 38], [2, 39], [2, 40], [2, 48], [2, 53], [2, 55], [2, 57], [3, 7], [3, 17]... | null | null | null | {"cover": [0, 1, 2, 4, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 20, 23, 24, 26, 27, 28, 32, 33, 35, 36, 39, 40, 41, 43, 44, 45, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59]} | 1 |
construct-mc-vertex-cover-l4-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 311 edges:
(0,2), (0,4), (0,12), (0,13), (0,15), (0,23), (0,27), (0,38), (0,44), (0,49), (0,54), (1,2), (1,4), (1,9), (1,22), (1,24), (1,25), (1,34), (1,35), (1,39), (1,43), (1,51), (1,56), (1,58), (2,14), (2,21), (2,24), (2,25), (2,30), (2,51), (2,53), (2,57), (2,59), (3,11)... | {"n": 60, "k": 41, "edges": [[0, 2], [0, 4], [0, 12], [0, 13], [0, 15], [0, 23], [0, 27], [0, 38], [0, 44], [0, 49], [0, 54], [1, 2], [1, 4], [1, 9], [1, 22], [1, 24], [1, 25], [1, 34], [1, 35], [1, 39], [1, 43], [1, 51], [1, 56], [1, 58], [2, 14], [2, 21], [2, 24], [2, 25], [2, 30], [2, 51], [2, 53], [2, 57], [2, 59],... | null | null | null | {"cover": [0, 1, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 32, 33, 34, 35, 38, 40, 41, 44, 45, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59]} | 1 |
construct-mc-vertex-cover-l4-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 334 edges:
(0,11), (0,18), (0,20), (0,22), (0,24), (0,25), (0,34), (0,38), (0,40), (0,42), (0,43), (0,46), (0,52), (0,55), (1,2), (1,7), (1,8), (1,19), (1,26), (1,27), (1,28), (1,50), (1,51), (1,54), (2,11), (2,15), (2,17), (2,18), (2,20), (2,21), (2,26), (2,36), (2,44), (2,5... | {"n": 60, "k": 41, "edges": [[0, 11], [0, 18], [0, 20], [0, 22], [0, 24], [0, 25], [0, 34], [0, 38], [0, 40], [0, 42], [0, 43], [0, 46], [0, 52], [0, 55], [1, 2], [1, 7], [1, 8], [1, 19], [1, 26], [1, 27], [1, 28], [1, 50], [1, 51], [1, 54], [2, 11], [2, 15], [2, 17], [2, 18], [2, 20], [2, 21], [2, 26], [2, 36], [2, 44... | null | null | null | {"cover": [0, 2, 3, 5, 7, 8, 9, 12, 13, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 40, 43, 45, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58]} | 1 |
construct-mc-vertex-cover-l4-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 338 edges:
(0,1), (0,3), (0,12), (0,21), (0,29), (0,36), (0,39), (0,44), (0,48), (0,51), (0,53), (0,56), (1,2), (1,9), (1,19), (1,24), (1,25), (1,30), (1,33), (1,38), (1,41), (1,42), (1,50), (1,52), (1,53), (1,57), (2,10), (2,30), (2,41), (2,42), (2,50), (3,4), (3,6), (3,9), ... | {"n": 60, "k": 41, "edges": [[0, 1], [0, 3], [0, 12], [0, 21], [0, 29], [0, 36], [0, 39], [0, 44], [0, 48], [0, 51], [0, 53], [0, 56], [1, 2], [1, 9], [1, 19], [1, 24], [1, 25], [1, 30], [1, 33], [1, 38], [1, 41], [1, 42], [1, 50], [1, 52], [1, 53], [1, 57], [2, 10], [2, 30], [2, 41], [2, 42], [2, 50], [3, 4], [3, 6], ... | null | null | null | {"cover": [1, 3, 4, 8, 9, 10, 12, 13, 14, 19, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59]} | 1 |
construct-mc-vertex-cover-l4-s6 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 260 edges:
(0,9), (0,14), (0,15), (0,24), (0,26), (0,28), (0,33), (0,35), (0,38), (0,39), (0,52), (0,55), (0,58), (1,3), (1,9), (1,14), (1,15), (1,20), (1,23), (1,24), (1,30), (1,33), (1,35), (1,42), (1,43), (1,48), (1,58), (1,59), (2,9), (2,14), (2,19), (2,23), (2,24), (2,33... | {"n": 60, "k": 41, "edges": [[0, 9], [0, 14], [0, 15], [0, 24], [0, 26], [0, 28], [0, 33], [0, 35], [0, 38], [0, 39], [0, 52], [0, 55], [0, 58], [1, 3], [1, 9], [1, 14], [1, 15], [1, 20], [1, 23], [1, 24], [1, 30], [1, 33], [1, 35], [1, 42], [1, 43], [1, 48], [1, 58], [1, 59], [2, 9], [2, 14], [2, 19], [2, 23], [2, 24]... | null | null | null | {"cover": [0, 1, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 33, 34, 38, 39, 40, 41, 44, 45, 46, 47, 49, 51, 52, 53, 56, 57, 58, 59]} | 1 |
construct-mc-vertex-cover-l4-s7 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 309 edges:
(0,5), (0,13), (0,20), (0,22), (0,32), (0,44), (0,48), (0,56), (0,57), (1,12), (1,16), (1,20), (1,37), (1,38), (1,50), (1,51), (1,53), (2,4), (2,24), (2,25), (2,27), (2,31), (2,35), (2,46), (2,47), (2,54), (3,15), (3,16), (3,24), (3,27), (3,28), (3,31), (3,34), (3,... | {"n": 60, "k": 41, "edges": [[0, 5], [0, 13], [0, 20], [0, 22], [0, 32], [0, 44], [0, 48], [0, 56], [0, 57], [1, 12], [1, 16], [1, 20], [1, 37], [1, 38], [1, 50], [1, 51], [1, 53], [2, 4], [2, 24], [2, 25], [2, 27], [2, 31], [2, 35], [2, 46], [2, 47], [2, 54], [3, 15], [3, 16], [3, 24], [3, 27], [3, 28], [3, 31], [3, 3... | null | null | null | {"cover": [1, 2, 3, 4, 5, 6, 7, 10, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 26, 29, 30, 31, 32, 33, 34, 35, 38, 39, 41, 44, 45, 46, 47, 48, 50, 51, 53, 54, 56, 57, 58]} | 1 |
construct-mc-vertex-cover-l4-s8 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 327 edges:
(0,4), (0,11), (0,12), (0,21), (0,25), (0,29), (0,47), (1,3), (1,9), (1,10), (1,18), (1,26), (1,31), (1,38), (1,41), (1,42), (1,43), (1,48), (1,49), (1,58), (1,59), (2,4), (2,15), (2,19), (2,29), (2,38), (2,42), (3,7), (3,8), (3,9), (3,10), (3,11), (3,18), (3,22), ... | {"n": 60, "k": 41, "edges": [[0, 4], [0, 11], [0, 12], [0, 21], [0, 25], [0, 29], [0, 47], [1, 3], [1, 9], [1, 10], [1, 18], [1, 26], [1, 31], [1, 38], [1, 41], [1, 42], [1, 43], [1, 48], [1, 49], [1, 58], [1, 59], [2, 4], [2, 15], [2, 19], [2, 29], [2, 38], [2, 42], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 18], [... | null | null | null | {"cover": [1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 29, 30, 33, 35, 37, 38, 41, 42, 43, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58]} | 1 |
construct-mc-vertex-cover-l4-s9 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 349 edges:
(0,6), (0,7), (0,10), (0,12), (0,14), (0,16), (0,24), (0,25), (0,26), (0,31), (0,34), (0,46), (0,56), (1,6), (1,8), (1,11), (1,12), (1,13), (1,17), (1,28), (1,32), (1,33), (1,35), (1,36), (1,43), (1,56), (1,59), (2,5), (2,6), (2,15), (2,24), (2,27), (2,31), (2,34),... | {"n": 60, "k": 41, "edges": [[0, 6], [0, 7], [0, 10], [0, 12], [0, 14], [0, 16], [0, 24], [0, 25], [0, 26], [0, 31], [0, 34], [0, 46], [0, 56], [1, 6], [1, 8], [1, 11], [1, 12], [1, 13], [1, 17], [1, 28], [1, 32], [1, 33], [1, 35], [1, 36], [1, 43], [1, 56], [1, 59], [2, 5], [2, 6], [2, 15], [2, 24], [2, 27], [2, 31], ... | null | null | null | {"cover": [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 18, 20, 22, 23, 24, 25, 26, 27, 28, 31, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 49, 51, 53, 56, 57, 58, 59]} | 1 |
construct-mc-vertex-cover-l5-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 529 edges:
(0,2), (0,6), (0,9), (0,10), (0,12), (0,34), (0,53), (0,59), (0,63), (0,70), (0,84), (1,16), (1,18), (1,22), (1,26), (1,52), (1,58), (1,74), (1,78), (2,16), (2,18), (2,21), (2,22), (2,25), (2,26), (2,37), (2,38), (2,43), (2,44), (2,50), (2,52), (2,67), (2,68), (3,1... | {"n": 90, "k": 63, "edges": [[0, 2], [0, 6], [0, 9], [0, 10], [0, 12], [0, 34], [0, 53], [0, 59], [0, 63], [0, 70], [0, 84], [1, 16], [1, 18], [1, 22], [1, 26], [1, 52], [1, 58], [1, 74], [1, 78], [2, 16], [2, 18], [2, 21], [2, 22], [2, 25], [2, 26], [2, 37], [2, 38], [2, 43], [2, 44], [2, 50], [2, 52], [2, 67], [2, 68... | null | null | null | {"cover": [0, 3, 6, 9, 11, 12, 13, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 80, 82, 83, 85, 86, 87]} | 1 |
construct-mc-vertex-cover-l5-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 575 edges:
(0,1), (0,2), (0,18), (0,28), (0,35), (0,37), (0,66), (0,74), (0,83), (1,2), (1,9), (1,12), (1,18), (1,33), (1,40), (1,41), (1,46), (1,69), (1,72), (1,77), (1,86), (1,88), (2,15), (2,20), (2,23), (2,29), (2,33), (2,52), (2,57), (2,58), (2,65), (2,84), (2,88), (3,7)... | {"n": 90, "k": 63, "edges": [[0, 1], [0, 2], [0, 18], [0, 28], [0, 35], [0, 37], [0, 66], [0, 74], [0, 83], [1, 2], [1, 9], [1, 12], [1, 18], [1, 33], [1, 40], [1, 41], [1, 46], [1, 69], [1, 72], [1, 77], [1, 86], [1, 88], [2, 15], [2, 20], [2, 23], [2, 29], [2, 33], [2, 52], [2, 57], [2, 58], [2, 65], [2, 84], [2, 88]... | null | null | null | {"cover": [1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 15, 18, 19, 21, 22, 23, 24, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 43, 44, 47, 48, 49, 50, 51, 53, 55, 56, 58, 59, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 89]} | 1 |
construct-mc-vertex-cover-l5-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 558 edges:
(0,4), (0,15), (0,20), (0,23), (0,43), (0,48), (0,56), (0,59), (0,65), (0,66), (0,71), (0,79), (0,80), (0,81), (0,84), (0,86), (1,3), (1,4), (1,6), (1,7), (1,11), (1,23), (1,24), (1,28), (1,37), (1,52), (1,59), (1,63), (1,64), (1,74), (1,77), (1,78), (2,20), (2,29)... | {"n": 90, "k": 63, "edges": [[0, 4], [0, 15], [0, 20], [0, 23], [0, 43], [0, 48], [0, 56], [0, 59], [0, 65], [0, 66], [0, 71], [0, 79], [0, 80], [0, 81], [0, 84], [0, 86], [1, 3], [1, 4], [1, 6], [1, 7], [1, 11], [1, 23], [1, 24], [1, 28], [1, 37], [1, 52], [1, 59], [1, 63], [1, 64], [1, 74], [1, 77], [1, 78], [2, 20],... | null | null | null | {"cover": [0, 1, 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 32, 34, 35, 36, 37, 39, 41, 42, 45, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 75, 77, 78, 80, 83, 84, 86, 87, 88]} | 1 |
construct-mc-vertex-cover-l5-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 551 edges:
(0,13), (0,19), (0,20), (0,25), (0,31), (0,32), (0,33), (0,38), (0,48), (0,56), (0,60), (0,69), (0,75), (0,89), (1,35), (1,36), (1,41), (1,46), (1,47), (1,56), (1,62), (1,76), (1,80), (1,89), (2,5), (2,13), (2,18), (2,20), (2,25), (2,30), (2,35), (2,41), (2,57), (2... | {"n": 90, "k": 63, "edges": [[0, 13], [0, 19], [0, 20], [0, 25], [0, 31], [0, 32], [0, 33], [0, 38], [0, 48], [0, 56], [0, 60], [0, 69], [0, 75], [0, 89], [1, 35], [1, 36], [1, 41], [1, 46], [1, 47], [1, 56], [1, 62], [1, 76], [1, 80], [1, 89], [2, 5], [2, 13], [2, 18], [2, 20], [2, 25], [2, 30], [2, 35], [2, 41], [2, ... | null | null | null | {"cover": [0, 2, 4, 5, 7, 8, 9, 12, 14, 15, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 32, 35, 36, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 58, 61, 62, 63, 64, 65, 66, 67, 68, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82, 85, 86, 87, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 543 edges:
(0,3), (0,5), (0,28), (0,29), (0,33), (0,35), (0,48), (0,58), (0,72), (0,73), (0,78), (1,9), (1,14), (1,15), (1,20), (1,27), (1,31), (1,32), (1,34), (1,35), (1,40), (1,41), (1,47), (1,52), (1,54), (1,57), (1,60), (1,81), (1,82), (1,86), (2,3), (2,4), (2,7), (2,10),... | {"n": 90, "k": 63, "edges": [[0, 3], [0, 5], [0, 28], [0, 29], [0, 33], [0, 35], [0, 48], [0, 58], [0, 72], [0, 73], [0, 78], [1, 9], [1, 14], [1, 15], [1, 20], [1, 27], [1, 31], [1, 32], [1, 34], [1, 35], [1, 40], [1, 41], [1, 47], [1, 52], [1, 54], [1, 57], [1, 60], [1, 81], [1, 82], [1, 86], [2, 3], [2, 4], [2, 7], ... | null | null | null | {"cover": [0, 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 15, 18, 19, 20, 22, 23, 24, 25, 26, 29, 30, 31, 36, 38, 40, 42, 44, 45, 46, 47, 48, 50, 52, 53, 55, 58, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 547 edges:
(0,5), (0,9), (0,17), (0,30), (0,35), (0,43), (0,45), (0,47), (0,50), (0,66), (0,67), (0,68), (0,73), (0,83), (1,8), (1,13), (1,23), (1,41), (1,50), (1,59), (1,60), (1,61), (1,75), (1,83), (2,6), (2,10), (2,25), (2,63), (2,67), (2,75), (2,76), (2,77), (2,81), (3,11... | {"n": 90, "k": 63, "edges": [[0, 5], [0, 9], [0, 17], [0, 30], [0, 35], [0, 43], [0, 45], [0, 47], [0, 50], [0, 66], [0, 67], [0, 68], [0, 73], [0, 83], [1, 8], [1, 13], [1, 23], [1, 41], [1, 50], [1, 59], [1, 60], [1, 61], [1, 75], [1, 83], [2, 6], [2, 10], [2, 25], [2, 63], [2, 67], [2, 75], [2, 76], [2, 77], [2, 81]... | null | null | null | {"cover": [0, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 18, 19, 20, 21, 23, 25, 30, 31, 32, 34, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 80, 81, 82, 83, 86, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s6 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 589 edges:
(0,6), (0,7), (0,8), (0,18), (0,27), (0,28), (0,46), (0,51), (0,64), (0,67), (0,69), (0,75), (0,77), (0,87), (0,89), (1,7), (1,12), (1,14), (1,18), (1,22), (1,45), (1,51), (1,58), (1,59), (1,60), (1,63), (1,65), (1,66), (1,68), (1,87), (1,88), (2,19), (2,23), (2,57... | {"n": 90, "k": 63, "edges": [[0, 6], [0, 7], [0, 8], [0, 18], [0, 27], [0, 28], [0, 46], [0, 51], [0, 64], [0, 67], [0, 69], [0, 75], [0, 77], [0, 87], [0, 89], [1, 7], [1, 12], [1, 14], [1, 18], [1, 22], [1, 45], [1, 51], [1, 58], [1, 59], [1, 60], [1, 63], [1, 65], [1, 66], [1, 68], [1, 87], [1, 88], [2, 19], [2, 23]... | null | null | null | {"cover": [0, 1, 2, 3, 5, 7, 8, 9, 11, 12, 14, 16, 17, 18, 19, 21, 22, 24, 26, 27, 28, 29, 30, 31, 32, 35, 38, 39, 40, 42, 44, 47, 48, 49, 51, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 78, 81, 82, 83, 84, 85, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s7 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 544 edges:
(0,2), (0,5), (0,6), (0,22), (0,26), (0,46), (0,54), (0,55), (0,60), (0,83), (0,84), (1,4), (1,11), (1,12), (1,19), (1,20), (1,36), (1,42), (1,44), (1,53), (1,54), (1,55), (1,56), (1,58), (1,62), (1,73), (1,79), (1,83), (1,84), (1,86), (2,18), (2,28), (2,33), (2,44... | {"n": 90, "k": 63, "edges": [[0, 2], [0, 5], [0, 6], [0, 22], [0, 26], [0, 46], [0, 54], [0, 55], [0, 60], [0, 83], [0, 84], [1, 4], [1, 11], [1, 12], [1, 19], [1, 20], [1, 36], [1, 42], [1, 44], [1, 53], [1, 54], [1, 55], [1, 56], [1, 58], [1, 62], [1, 73], [1, 79], [1, 83], [1, 84], [1, 86], [2, 18], [2, 28], [2, 33]... | null | null | null | {"cover": [0, 1, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 54, 57, 58, 60, 61, 65, 67, 70, 71, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s8 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 515 edges:
(0,1), (0,6), (0,16), (0,22), (0,24), (0,41), (0,49), (0,55), (0,63), (0,67), (0,71), (0,79), (0,83), (0,87), (0,88), (1,23), (1,28), (1,46), (1,62), (1,66), (1,70), (2,10), (2,16), (2,18), (2,20), (2,25), (2,27), (2,41), (2,55), (2,74), (3,8), (3,9), (3,11), (3,44... | {"n": 90, "k": 63, "edges": [[0, 1], [0, 6], [0, 16], [0, 22], [0, 24], [0, 41], [0, 49], [0, 55], [0, 63], [0, 67], [0, 71], [0, 79], [0, 83], [0, 87], [0, 88], [1, 23], [1, 28], [1, 46], [1, 62], [1, 66], [1, 70], [2, 10], [2, 16], [2, 18], [2, 20], [2, 25], [2, 27], [2, 41], [2, 55], [2, 74], [3, 8], [3, 9], [3, 11]... | null | null | null | {"cover": [0, 1, 2, 5, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 22, 23, 24, 25, 28, 29, 31, 32, 33, 35, 36, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 65, 67, 71, 72, 73, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 88, 89]} | 1 |
construct-mc-vertex-cover-l5-s9 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 577 edges:
(0,14), (0,16), (0,31), (0,39), (0,44), (0,46), (0,57), (0,60), (0,71), (0,74), (0,76), (0,80), (0,81), (1,7), (1,10), (1,11), (1,15), (1,30), (1,31), (1,44), (1,45), (1,53), (1,58), (1,62), (1,64), (1,71), (2,7), (2,11), (2,22), (2,23), (2,38), (2,40), (2,49), (2,... | {"n": 90, "k": 63, "edges": [[0, 14], [0, 16], [0, 31], [0, 39], [0, 44], [0, 46], [0, 57], [0, 60], [0, 71], [0, 74], [0, 76], [0, 80], [0, 81], [1, 7], [1, 10], [1, 11], [1, 15], [1, 30], [1, 31], [1, 44], [1, 45], [1, 53], [1, 58], [1, 62], [1, 64], [1, 71], [2, 7], [2, 11], [2, 22], [2, 23], [2, 38], [2, 40], [2, 4... | null | null | null | {"cover": [0, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 20, 21, 22, 23, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 53, 54, 57, 58, 59, 61, 62, 64, 66, 67, 68, 71, 73, 76, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89]} | 1 |
construct-mc-vertex-cover-l6-s0 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1392 edges:
(0,7), (0,8), (0,12), (0,18), (0,30), (0,43), (0,45), (0,56), (0,73), (0,79), (0,83), (0,84), (0,95), (0,100), (0,103), (0,114), (0,115), (0,128), (1,3), (1,8), (1,10), (1,28), (1,32), (1,37), (1,38), (1,41), (1,50), (1,51), (1,54), (1,55), (1,58), (1,60), (1,64... | {"n": 140, "k": 107, "edges": [[0, 7], [0, 8], [0, 12], [0, 18], [0, 30], [0, 43], [0, 45], [0, 56], [0, 73], [0, 79], [0, 83], [0, 84], [0, 95], [0, 100], [0, 103], [0, 114], [0, 115], [0, 128], [1, 3], [1, 8], [1, 10], [1, 28], [1, 32], [1, 37], [1, 38], [1, 41], [1, 50], [1, 51], [1, 54], [1, 55], [1, 58], [1, 60], ... | null | null | null | {"cover": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 25, 26, 27, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 53, 54, 55, 56, 57, 58, 60, 63, 65, 66, 67, 68, 69, 71, 72, 73, 77, 79, 80, 81, 83, 84, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 10... | 1 |
construct-mc-vertex-cover-l6-s1 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1439 edges:
(0,4), (0,5), (0,7), (0,11), (0,13), (0,14), (0,15), (0,18), (0,34), (0,35), (0,38), (0,39), (0,42), (0,43), (0,48), (0,49), (0,56), (0,72), (0,76), (0,78), (0,84), (0,98), (0,107), (0,112), (0,122), (0,132), (0,136), (0,138), (1,6), (1,10), (1,13), (1,17), (1,1... | {"n": 140, "k": 107, "edges": [[0, 4], [0, 5], [0, 7], [0, 11], [0, 13], [0, 14], [0, 15], [0, 18], [0, 34], [0, 35], [0, 38], [0, 39], [0, 42], [0, 43], [0, 48], [0, 49], [0, 56], [0, 72], [0, 76], [0, 78], [0, 84], [0, 98], [0, 107], [0, 112], [0, 122], [0, 132], [0, 136], [0, 138], [1, 6], [1, 10], [1, 13], [1, 17],... | null | null | null | {"cover": [0, 1, 3, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 36, 37, 38, 40, 42, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 74, 77, 78, 80, 81, 82, 83, 84, 85, 87, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 103, 1... | 1 |
construct-mc-vertex-cover-l6-s2 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1360 edges:
(0,5), (0,14), (0,23), (0,45), (0,47), (0,60), (0,61), (0,69), (0,73), (0,86), (0,87), (0,98), (0,100), (0,106), (0,115), (0,116), (0,117), (0,132), (1,10), (1,19), (1,55), (1,60), (1,86), (1,91), (1,95), (1,99), (1,102), (1,108), (1,109), (1,113), (1,135), (1,1... | {"n": 140, "k": 107, "edges": [[0, 5], [0, 14], [0, 23], [0, 45], [0, 47], [0, 60], [0, 61], [0, 69], [0, 73], [0, 86], [0, 87], [0, 98], [0, 100], [0, 106], [0, 115], [0, 116], [0, 117], [0, 132], [1, 10], [1, 19], [1, 55], [1, 60], [1, 86], [1, 91], [1, 95], [1, 99], [1, 102], [1, 108], [1, 109], [1, 113], [1, 135], ... | null | null | null | {"cover": [0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 72, 73, 74, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 103,... | 1 |
construct-mc-vertex-cover-l6-s3 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1389 edges:
(0,1), (0,25), (0,26), (0,31), (0,47), (0,55), (0,57), (0,59), (0,67), (0,80), (0,101), (0,112), (0,119), (0,127), (0,131), (0,135), (0,136), (1,2), (1,9), (1,15), (1,25), (1,27), (1,31), (1,34), (1,45), (1,49), (1,51), (1,52), (1,63), (1,68), (1,77), (1,98), (1... | {"n": 140, "k": 107, "edges": [[0, 1], [0, 25], [0, 26], [0, 31], [0, 47], [0, 55], [0, 57], [0, 59], [0, 67], [0, 80], [0, 101], [0, 112], [0, 119], [0, 127], [0, 131], [0, 135], [0, 136], [1, 2], [1, 9], [1, 15], [1, 25], [1, 27], [1, 31], [1, 34], [1, 45], [1, 49], [1, 51], [1, 52], [1, 63], [1, 68], [1, 77], [1, 98... | null | null | null | {"cover": [0, 1, 2, 3, 4, 5, 7, 9, 11, 12, 14, 15, 18, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 38, 39, 41, 42, 43, 45, 46, 47, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 78, 80, 81, 82, 83, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 1... | 1 |
construct-mc-vertex-cover-l6-s4 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1332 edges:
(0,1), (0,6), (0,15), (0,20), (0,21), (0,26), (0,50), (0,59), (0,76), (0,85), (0,94), (0,96), (0,107), (0,108), (0,121), (0,122), (0,126), (0,127), (0,129), (1,6), (1,10), (1,27), (1,29), (1,30), (1,36), (1,56), (1,58), (1,67), (1,71), (1,76), (1,77), (1,90), (1... | {"n": 140, "k": 107, "edges": [[0, 1], [0, 6], [0, 15], [0, 20], [0, 21], [0, 26], [0, 50], [0, 59], [0, 76], [0, 85], [0, 94], [0, 96], [0, 107], [0, 108], [0, 121], [0, 122], [0, 126], [0, 127], [0, 129], [1, 6], [1, 10], [1, 27], [1, 29], [1, 30], [1, 36], [1, 56], [1, 58], [1, 67], [1, 71], [1, 76], [1, 77], [1, 90... | null | null | null | {"cover": [1, 2, 3, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 33, 34, 35, 36, 37, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 69, 70, 72, 74, 75, 76, 78, 79, 80, 81, 83, 85, 86, 87, 88, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 102, 103, 1... | 1 |
construct-mc-vertex-cover-l6-s5 | construct | mc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | MathConstraint/vertex_cover | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 1372 edges:
(0,2), (0,12), (0,15), (0,20), (0,24), (0,46), (0,50), (0,51), (0,52), (0,53), (0,62), (0,70), (0,95), (0,102), (0,117), (0,121), (0,127), (0,134), (1,3), (1,11), (1,16), (1,52), (1,53), (1,60), (1,64), (1,69), (1,79), (1,81), (1,90), (1,91), (1,98), (1,100), (1... | {"n": 140, "k": 107, "edges": [[0, 2], [0, 12], [0, 15], [0, 20], [0, 24], [0, 46], [0, 50], [0, 51], [0, 52], [0, 53], [0, 62], [0, 70], [0, 95], [0, 102], [0, 117], [0, 121], [0, 127], [0, 134], [1, 3], [1, 11], [1, 16], [1, 52], [1, 53], [1, 60], [1, 64], [1, 69], [1, 79], [1, 81], [1, 90], [1, 91], [1, 98], [1, 100... | null | null | null | {"cover": [2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 57, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 90, 91, 92, 94, 95, 96, 98, 99, 100, 101, 102, ... | 1 |
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